Fig. 1. Schematic of the anisotropic elementary unit and the working principle for the CVB converter. (a) The all-silicon unit configuration consisting of the bar and substrate. (b) The rotation angle θ of the bar is determined by the x axis and the length direction of the bar. (c) The principal diagram of regulating polarization based on the spin-decoupled phase control method where the black dotted lines represent the x axis.

Fig. 2. Simulation of transmission amplitude (txx, tyy), phase shift (φxx, φyy), and respective differences in the dependence of the bar sizes (a, b) at 1-THz incidence.

Fig. 3. Simulated amplitude (txx, tyy), amplitude difference (tyy−txx), phase shift (φxx, φyy), and phase-shift difference |φyy−φxx| as a function of the incident frequency, which confirms the property of the half-wave plate and the 2π dynamic phase coverage of 1–8 bars.

Fig. 4. Schematic of the transverse dual-focusing CVB system. The inset on the right illustrates the specific arrangement of metasurface elements.

Fig. 5. Simulation results of the transverse dual-focusing CVB system under the incidence of x-polarized light. (a) The distribution of E-field vectors on the x–y plane with z=1200  μm. (b) Total E-field intensity distribution on the x–z plane with y=0  μm. (c)–(f) E-field maps on the x–y plane with z=1200  μm. The black dashed line and the pink solid line in (b) indicate the x–y plane with z=1200  μm and the plane where the true radial polarizations are located, respectively.

Fig. 6. Schematic of the longitudinal dual-focusing CVB system. The top inset illustrates the arrangement of the bar elements.

Fig. 7. Simulation results of the longitudinal dual-focusing CVB system under the incidence of x-polarized light. (a) and (b) Distributions of E-field vectors on the x–y plane with z=1200  μm (focus f1) and 3300 μm (focus f2), respectively. (c)–(e) E-field maps on the x–z plane with y=0  μm.

Fig. 8. Simulation results of the longitudinal polarization-dependent dual-focusing CVB system under the incidence of y-polarized light. (a) and (b) E-field distributions on the x–y plane with z=1200  μm (focus f1) and 3300 μm (focus f2). (c)–(h) E-field intensity maps on the f1 and f2 focal planes.

Fig. 9. Calculation results of the optical force. (a) Schematic of the longitudinal dual-focusing CVB metalens and the glass sphere which is subjected to the optical force. (b) Calculated longitudinal optical force Fz of the RPVB focusing at f1 under x-polarized incident light. (c) and (d) Calculated transverse optical forces Fx and Fy of the APVB focusing at f1 under y-polarized incident light. The dashed lines in (b) and (c) indicate the focal plane. The insets in the lower left corners in (b)–(d) show E-field distributions at corresponding focal planes.